I’m debating a couple of undergraduate courses for the winter. Basically I can take either MATH 2505 Introductory Analysis or MATH 3210 Intro to Numerical Analysis not both and based on my subsequent two years I probably won’t be able to return to do the one I pass on. 2505 is an Honors class (iz fine) and a prerequisite for some serious Analysis classes, yet I am planning on focusing on Abstract Algebra (perhaps in some ways it’s more relevant to doing CS research) and wouldn’t necessarily take advanced Analysis on personal interest alone.

Another stream of courses I take leads me through stat theory to fourth year Bayesian Data Analysis, also my major is CS so I get data structures and algorithms, but curiously we don’t have formal numerical analysis.

Here are some course definitions:

2505 - “Axioms for the real number system, geometry and topology of Euclidean space, limits, continuity, differentiability, the inverse and implicit function theorems.”

|_ 3501 - “Metric spaces, point-set topological notions, sequences, completeness, separability, compactness (Heine-Borel, Bolzano-Weierstrass, Finite Intersection, complete and totally bounded), limits and continuity, continuity in topological terms, connectedness, path and local-path connectedness, homeomorphisms, uniform continuity, Lipschitz continuity, contractions, contraction principle, sequences of functions, uniform convergence.”

|_ 3502 - “The full derivative for functions between Euclidean spaces, directional derivatives, Jacobian matrix, differentiability, C¹ functions, multilinear maps, higher derivatives, Taylor’s theorem, extrema, inverse and implicit function theorems, extrema subject to constraints, Lagrange multipliers.”

3210 - “Root finding, interpolation, integration, initial value problems, linear and nonlinear fitting, boundary value problems, error analysis and stability of methods, as well as practical computer implementation.”

My interest is to research and contribute new functions into the Stan math library, which course of the two would you recommend as more rewarding (even indirectly)? Is it a mistake in the Stan/BDA world to avoid Analysis in favor of Algebra? Which course would you take?

I’m really totally split on the decision.